Sources told the US-based sports network on Thursday the fight would be staged in Las Vegas on July 19.
Pacquiao, who won 12 world titles in eight different weight classes, has not fought since dropping a unanimous 12-round decision to Cuban Yordenis Ugas for the WBA welterweight crown on August 21, 2021, in Las Vegas.
ESPN reported that WBC president Mauricio Sulaiman said last week at a fight in Saudi Arabia that Pacquiao planned to fight Barrios for the crown in July and the Asian star had already been cleared to fight by the Nevada State Athletic Commission.
WBC rules allow a former champion to request a world title fight when coming out of retirement.
Pacquiao is set to be inducted into the International Boxing Hall of Fame next month and faces a Senate election next week in the Philippines.
Barrios is 29-2 with one drawn and 18 knockouts and kept his title in November with a draw against fellow American Abel Ramos in his most recent bout on the Mike Tyson-Jake Paul undercard.
Pacquiao has a career record of 62-8 with two drawn and 39 knockouts. (AFP)
